The concept and design of a relativistic two-cavity reflex klystron with a magnetic mirror is proposed. A 2.5-D computer particle-in-cell (PIC) model of a relativistic two-cavity reflex klystron with magnetic mirror based on the KARAT PIC code was created. The model takes into account the input of an external microwave from the master oscillator, allows self-consistent calculation of the electron dynamics and output characteristic of the klystron. Comparative simulation of relativistic two-cavity reflex klystron with magnetic mirror and relativistic two-cavity transit klystron without magnetic mirror was carried out. It was been shown that the spectral characteristics of both klystrons are close. The output power of the reflex klystron and the transit klystron are compared. It was found that the output power of the reflex klystron is about 1.4 times more that of the transit klystron. The influence of magnetic mirror position on the value of the generated microwave power of the reflex klystron has been studied.

Monitoring of the greenhouse gases concentrations and their dynamics is a fundamental and crucial task in environmental monitoring. Gases such as water vapor, carbon dioxide, methane, and others enter the atmosphere through both natural processes and anthropogenic activities. The accumulation of these gases enhances the greenhouse effect, negatively impacting human health, agriculture, and the environment as a whole.  Therefore, the development of devices capable of determining atmospheric greenhouse gas concentrations is vital. Optical measurement methods, including nondispersive infrared (NDIR) spectroscopy, offer non-contact and automated measurement of gaseous mixture components. The NDIR gas analyzer presented in this work registers radiation at a wavelength of 4.26 µm to determine carbon dioxide concentration (with provision for water vapor detection). The resulting signal is normalized using a reference channel tuned to 3.95 µm. The mathematical model, developed using MATLAB and Python programming languages, processes the experimental data to determine atmospheric carbon dioxide concentrations. The developed device is an open-path gas analyzer, enabling its use in diverse environments due to its reduced power consumption.  This instrument is applicable for carbon polygon monitoring and for quality control of low-Earth orbit satellites performing atmospheric greenhouse gases monitoring.

A new mathematical model based on the nonlinear Schrödinger equation with six arbitrary functions and allowing for various factors is presented. This multifunctional model is a broad generalization of numerous simpler related nonlinear models that are commonly encountered in various areas of theoretical physics, including nonlinear optics, superconductivity, and plasma physics. To analyze the nonlinear equation under consideration, a combination of the method of functional constraints and methods of generalized separation of variables is used. One-dimensional non-symmetry reductions are described, which lead the studied complex partial differential equation to simpler ordinary differential equations or systems of such equations. A number of exact solutions of the nonlinear Schrödinger equation of general form have been found, which are expressed in quadratures or elementary functions. Both periodic solutions in time and in spatial variable are obtained. Special attention is paid to some narrower classes of nonlinear PDEs with a smaller number of arbitrary functions. The described general multifunctional model allows one to effectively analyze numerous simpler models by specifying a specific particular forms of arbitrary functions. The exact solutions obtained in this work can be used as test problems intended to check the adequacy and assess the accuracy of numerical and approximate analytical methods for integrating nonlinear equations of mathematical physics.

The article considers the problem of detecting abnormal outliers and mitigating their negative impact on the estimates of the allocated characteristics of the calculated indicators. To solve the problem, the article considers various robust methods used in practice and computational schemes for detecting abnormal outliers in the values ​​of the studied indicators based on them. A comparison is made of the efficiency of detecting abnormal outliers by various methods for samples of random variables with a normal distribution law for various options for the number and location of abnormal outliers in relation to non-anomalous values ​​using standard random variable sensors. The robust methods and schemes studied in the article are used to detect abnormal outliers in patient readings and ventilation flow parameters during artificial lung ventilation (ALV). The numerical experiments conducted, the results of which are presented in this article, showed that the most effective method for detecting abnormal outliers with an unknown variance of the main part of non-anomalous data is the modified Huber method developed at MEPhI. This method allows us to effectively identify abnormal emissions from the formed database of clinical experience in treating patients on ventilators, which makes it possible to use this method to create a stable scheme for selecting optimal values ​​of ventilation flow indicators depending on the values ​​of the indicators of the patient's current condition.

Singular spectrum analysis is successfully applied in many practical problems of mathematical modeling, including economic ones. The purpose of this work is to develop a new mathematical approach for forecasting the values ​​of key performance indicators of credit institutions (“Profit”, “Accounts with the Bank of Russia”, “Securities”), presented as time series with an observation step of one month. The analysis and forecasting of key indicators was carried out using singular spectrum analysis by the “Caterpillar”-SSA method in the CaterpillarSSA program. The relevance of the study is due to the need to implement new efficient computing technologies for the early warning systems of the Bank of Russia and Rosfinmonitoring. The article presents the implementation of the “Caterpillar”-SSA method for assessing the financial condition of two types of credit institutions: a bank with a revoked license (JSC Bank “CCB”) and a reliable bank (JSC “TBank”). The authors managed to implement the decomposition of time series of key indicators into a trend, harmonic and noise components. Based on the principal components responsible for the trend and periodicity, the reconstruction and forecasting of the considered time series for 6 months ahead were performed with high accuracy

Modeling of atmospheric phenomena is carried out on the basis of systems of ordinary differential equations and partial differential equations with their subsequent numerical study. As a result of discretization of these equations, we arrive at systems with millions and even billions of unknowns. Due to the nonlinearity of the complete system of Navier-Stokes equations, constructing its solutions is quite labor-intensive. As a consequence, the linearization procedure is applied on the exact solution (homogeneous rest). For the linearized system, taking into account the action of gravity and Coriolis forces, the emergence and development of ascending swirling flows of different intensity is numerically modeled using blowing up the pipe. Numerical calculation of the velocity characteristics of a three-dimensional unsteady flow of viscous heat-conducting gas in an ascending swirling flow initiated by vertical blowing showed that the gas swirl occurs in the positive direction and is due to the presence of terms in the linearized complete system of Navier-Stokes equations describing the Coriolis acceleration. Thus, the pattern of the occurrence of an ascending swirling flow is once again numerically confirmed. A conclusion is also made about the possibility of applying this approach to the study of ascending swirling flows such as tornadoes and tropical cyclones

The rapid increase in cyberattacks targeting critical components of Russia’s information infrastructure — from banking systems and energy complexes to telecommunications networks — underscores the need for comprehensive and adaptive cybersecurity measures. This study aims to develop approaches that enable not only the efficient allocation of cybersecurity resources but also the prioritization of threats based on their criticality, which is especially important for protecting the system’s most vulnerable links. A detailed analysis of infrastructure vulnerabilities has been conducted, identifying key risk areas that require prioritized protection. Particular attention is given to the necessity of coordination between public and private sectors, as well as the integration of artificial intelligence technologies. Such technologies enhance both the accuracy of cyberattack forecasting and the efficiency of response actions. The study's findings emphasize the importance of implementing adaptive standards and multi-level collaboration for the effective protection of critical assets. This flexible, coordinated approach to cybersecurity strengthens the resilience of national infrastructure in the face of escalating cyber threats. Additionally, the integration of comprehensive technologies alongside standardized methods creates the potential for a flexible defense system capable of swiftly adapting to emerging threats and enabling continuous monitoring of critical assets.

A pressing issue today is to ensure fault tolerance in control systems operating under conditions of high-energy particle impact, such as cosmic radiation, consisting mainly of protons with energies up to  eV. There are quite a few such particles, but as a result of interaction with matter they produce neutrons, some of which, as a result of elastic collisions with silicon atoms (the main component of a modern microcircuit), produce primarily knocked-out atoms (PKAs) of sufficient energy to generate electron-hole pairs in a semiconductor, and they, acting on a working transistor, can cause a failure in the operation of the entire device. It is immediately clear that theoretical calculations here are greatly complicated by the complexity of the processes described above, and therefore experiments with real irradiation and measurement of the number of failures are needed. In this work, fault tolerance is experimentally investigated when an integrated circuit is exposed to Pu-Be source neutrons with an average energy of about 3.8 MeV. An experimental setup is developed that records the number of faults in the circuit when irradiated. The possibility of increasing the fault tolerance of FPGA circuits by using redundancy (spatial and temporal triplication) is demonstrated